The elderly woman - who is said to be disabled - was attacked at a rented thatched bungalow at Ras Kitau.

Witnesses said they heard shots being fired before the woman was taken away in a motorboat.

The attack comes three weeks after a British couple were attacked further north in Kiwayu. Gunman shot dead the husband and kidnapped his wife.

The British woman, Judith Tebbutt, was taken across the border to Somalia, where she is still being held.

'Hugely damaging'

The gunmen struck at Ras Kitau after midnight. Witnesses say they heard at least two gunshots before the woman was taken away by the attackers. "Armed people came into Manda by boat in the middle of the night. The elderly French woman is well known in the area, she comes to Manda regularly," Abu Chiaba, a local legislator, told Reuters.

Kenyan police have not released the name of the woman. The attack happened just across a lagoon from Shela - an exclusive resort on Lamu island. It could be hugely damaging to Lamu's tourism industry, the BBC's Will Ross in Nairobi says.